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Register a new userProperties and approximation of functions in the class of functions
خواص و تقريب الدوال في صف الدوال
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Tishreen University ورقة بحثية
Publication date
2016
fields
Technical Architecture
and research's language is
العربية
Authors
نزار محمد حسن( باحث )
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Shamra Editor
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درسنا في هذه المقالة إحدى مسائل التحليل الدالي المتعلقة بإنشاء صف دالي جديد نرمز له بـالرمز انطلاقاً من تعريف كلٍ من صف دوال ليبيغ و صف دوال هولدر و من ثم درسنا علاقات التداخل في هذا الصف و العلاقة بين الصف الجديد و كلٍ من صفي دوال ليبيغ و دوالهولدر، في النهاية ندرس تقريب صف الدوال الجديد إلى دوال كسرية.
We study in this paper one of functional analysis problems, involved with construction a new class of functions, denoted by . The definition of the new class depends on definition of Lebesgueclass of functions and on the Holder clas . We study the relation between the new class and approximation of the new class to rational functions.
References used
BÖTTCHER.A; KARLOVICH.A.Y. Carleson Curves, Muckenhoupt Weights, and ToeplitzOperators.Springer Basel AG, Washington D.C, 1997, 407
DAVID.G. Operateursintegrauxsingulerssurcertainescourbes du plan complexe. Vol 17 (4), Ann. Sci. Ecole Norm. Sup, 1984, 157-189
ISRAFILOV. D.M. Approximation by p-faber polynomials in the weighted smirnov class E (G,W) p and Bieberbach Polynomials. Vol 17,Constr.Approx. 2001, 335- 351
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The aim of this research is to present the two new classes of complex functions . The first class is denoted , and the second one is denoted. The definition of both of them depends on the famous Lebesgue class ,and orlicz class .The relationship bet
ween the two new classes the two classes is studied. This study gives some properties .
Finally, this study is used for approximation of the class on group of wide curves.
This research aimed to define a new class of complex functions , which depends in its definition on the definition of famous Holder class. We studied the relation between the new and Holder classes, then we proved some properties of the class.
We fi
nally applied this study to approximate the class of complex functions on closed curves , which belong to a wide class of curves.
We study in this research approximation of complex functions from Orlicz space on a subclass of Carlson curves, which called Dini smooth curves to rational functions by using polynomials related with Dzjadyk sums which obtained from Faber polynomials. We depend on some concepts of complex analysis such as formulas of Sokhotski to reach the desired goal
In this research, we have studied the issue of approximation of complex functions from weighted Lebesgue space ; and (Mukenhoupt weight) to rational functions by using p- Faber polynomials on large group of curves, which called Carlson curves. This
is also considered as a follow-up to the work done by researchers: Israfilov and Testici in 2014 , where they studied approximation of functions from weighted Smirnov space on domains with a Carlson curve boundary.
We study in this research some properties of wide class of curves, called k-curves, which is defined by a relation existing between arches and chords connecting any two arbitrary points on it
Especially we study the effect of some mappes on the curves of this class.
Then we study the approximation of weighted Holder class of function on k-curves.
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